RCD normalization conjecture for Hausdorff measure

Let $(X,\mathsf{d},\mathfrak{m})$ be an $\operatorname{RCD}(K,N)$ space. Suppose that, for some $b,k\in(0,\infty)$,

$$\mathfrak{m}=b\mathcal{H}^k.$$

RCD normalization conjecture. Then $(X,\mathsf{d},\mathcal{H}^k)$ is a non-collapsed $\operatorname{RCD}(K,k)$ space. This is the RCD formulation of the paper's first conjecture and would show that proportionality of the reference measure to Hausdorff measure forces the corresponding non-collapsed RCD structure; the source gives no resolution.